modeling and simulation for free fall bomb dynamics in ... · pdf filemissile datcom computer...

Paper: ASAT-16-137-MO

16th

International Conference on

AEROSPACE SCIENCES & AVIATION TECHNOLOGY,

ASAT - 16 – May 26 - 28, 2015, E-Mail: [email protected]

Military Technical College, Kobry Elkobbah, Cairo, Egypt

Tel : +(202) 24025292 – 24036138, Fax: +(202) 22621908

Modeling and Simulation for Free Fall Bomb Dynamics in Windy

Environment

Aly S. Atallah1, Gamal A. El-Sheikh

2, Alaa El-Din S.Mohamedy

3, Ahmed T. Hafez

4

1 M.Sc. Candidate, Military Technical College, Egypt

2 Professor, Pyramids high institute for Engineering and Technology, Egypt

3 Dr, EAF Researches and Development Branch, Egypt

4 Dr, Military Technical College, Egypt

Abstract: The main goal of aircraft bombing is its success in the destruction of the required

target depending on the correct aiming and the correct moment of release. Different

conditions, such as air speed, altitude, angle of release and the presence of wind, have a

significant effect on the choice of the release moment to ensure target destruction. In this

paper, a Six-degree of freedom (6DOF) mathematical model for the free fall bomb is

presented describing the motion of the bomb in the three-dimensional space in the presence of

stochastic winds. The aerodynamic coefficients for the free fall bomb are calculated through

Missile Datcom computer program, however, these coefficients can be calculated either

experimentally using the wind tunnel or a flight test; or mathematically through the

Computational Fluid Dynamics (CFD). The stochastic wind affecting the trajectory of the

bomb is defined by a velocity spectral represented by the Continuous Dryden Spectral. The

contribution in this paper is the modeling and evaluation of the free fall bomb flight

simulation in the presence of stochastic wind affecting the bomb flight trajectory.

Keywords: Bomb, Missile Datcom, Wind model, Mathematical Model

1. Introduction

For several decades, there has been an enormous increase in carrying stores (both guided and

unguided weapons) on tactical fighter aircraft. In fact, many of today’s aircraft carry so many

stores such that pundits have remarked:"It is the stores that are carrying the aircraft! "[13]. As

part of the process of store delivery prediction and verification we are developing dynamic

model which can simulate the store release, and store ballistic behavior of unguided weapon.

The accuracy of store delivery depends on a number of factors, including aircraft release

conditions, store ejection characteristics, aerodynamic disturbances, store aerodynamic

characteristics and atmospheric disturbances.

The external ballistics deals with the part of bomb motion through the external medium and

its behavior during flight, i.e., from point of release to the impact point. There are different

approaches to simulate bomb trajectory models like Point Mass (PM), Modified Point Mass

(MPM) and 6DOF, which had developed for computing trajectory parameters and generation

of Range Tables (RTs) for conventional free bombs [3].


Dynamic characteristics of the bomb are normally described in terms of its stability derivative

values. Typically, these coefficients are experimentally obtained using wind tunnel or flight

test, or mathematically using CFD. Although wind tunnel testing results in fairly accurate

values of these coefficients, it is considered a complicated and time consuming method

because several scale, interference and dynamic effects must be taken into account during

refining its results. The second, and the most accurate method, involves flight testing the

actual bomb. Unfortunately, these tests are very expensive, risky and time consuming to

complete flight test program depending on number and type of required tests. The third

method is the CFD which employs a combination of data sheets, linear aerodynamic theory,

and empirical relations. This method provides less precision than the wind tunnel testing and

takes lots of CPU time particularly if estimates of coefficients are desired over a wide range

of flight conditions [8].

Nowadays, several software packages exist that allow one to obtain rapid, economical and

reasonably good estimation of aerodynamic stability and control characteristics. Among these

software packages are Tornado, LinAir, AVL, Digital DATCOM and MISSILE DATCOM.

MISSILE DATCOM software developed by U.S. Air Force has been widely used for

preliminary estimation of bombs and missiles’ aerodynamic coefficients and stability

derivatives. Given the bomb configuration declared in an ASCI text file, MISSILE DATCOM

will easily provide the estimation of bomb’s aerodynamic coefficients and its stability

derivatives for a given atmospheric conditions [8, 9].

The paper is organized as follows: the second section defines different coordinate systems and

setting the 6DOF mathematical model for bomb trajectory, third section presents aerodynamic

coefficients of bomb with a brief description about MISSILE DATCOM software with its

input and output files, fourth section is devoted to wind disturbance model to study the effect

of windy environment on bomb trajectory, in fifth section, simulation results are introduced

for bomb flight data evaluation and bomb behavior in atmospheric disturbance. Finally, the

paper concludes with a brief summery.

2. Problem formulation

2.1 Coordinate Systems

To formulate a 6DOF mathematical model of bomb, we define the following coordinate

systems [1];

OXbYbZb Bomb-Fixed coordinate system with its origin at bomb center of gravity (c.g.)

OXaYaZa Air-trajectory reference coordinate system.

OXgYgZg Earth-reference coordinate system.

These systems are related to each other by means of the Euler’s angles and the transformation

matrices.

Transformation between OXbYbZb and OXgYgZg systems: with the yaw angle , pitch angle

and roll angle ;

(1.a)


Fig.1a: Geometry between OXbYbZb and OXgYgZg systems

Transformation between OXbYbZb and OXaYaZa systems: with the angle of sideslip and

angle of attack ;

(1.b)

Fig.1b: Geometry between OXbYbZb and OXaYaZa systems

2.2 Equations of Motion

In order to describe the bomb flight path, 6DOF model is constructed under the following

assumptions [1, 7]:

1. The bomb is considered as a rigid body.

2. The Earth is considered flat, non rotary and the gravity acceleration is considered

constant.


3. The bomb mass and moment of inertia are considered constant during any particular

dynamic analysis and constant position of center of mass.

4. Both XZ plane and XY plane are planes of bomb symmetry.

5. Small azimuth angle.

6. The bomb is considered non-spinning.

7. Bomb is released from level flight.

Starting from Newton’s second low of motion, "The summation of all external forces and

moments acting on a body must equal to the time rate of change of its momentum and angular

momentum respectively." [1, 7 and 12], it is expressed in body frame by:

(2)

(3)

Where Tb rqpω , and is moment of inertia matrix.

Euler angles represent three successful rotations (roll, pitch and yaw). There is a direct

relationship between Euler angles and the angular velocity of the bomb around its body axes.

The rates of change of the attitude angles can be obtained as:

(4)

To fully describe the bomb trajectory, both orientation and position with respect to inertial

axes should be defined. The bomb linear velocities TwvuV must be converted into

linear position rates in earth axes by applying transformation from body axes to earth axes.

(5)

Forces acting on bomb are aerodynamic forces and weight force. Components of these forces

are represented in body frame as follows:

(6.a)

(6.b)

(7.a)

(7.b)


(7.c)

Where force vector is TZYXF , the weight force Tzyx WWWW and

aerodynamic force vector is Tzyx RRRR .

On other hand, moments acting on bomb are only the aerodynamic moments which are

represented in body frame as follows:

(8)

Where the moment vector is TNMLM .

Considering assumptions, the 6DOF mathematical model will be as follows:

Force equations;

(9.a)

(9.b)

(9.c)

Moment equations;

(10.a)

(10.b)

(10.c)

Kinematic equations;

(11.a)

(11.b)

(11.c)

Navigation equations;

(12.a)

(12.b)

(12.c)

The model bomb characteristics are shown in Table 1 [10, 11].

Table 1 Bomb characteristics

Mass (m) 239.5 [Kg] Ixx 2.35 [Kg m2]

Diameter(D) 0.273 [m] Iyy 56.74 [Kg m2]

Length (l) 2.3 [m] Izz 56.74 [Kg m2]


3. Aerodynamic coefficients for forces and moments

The aerodynamic coefficients are called total coefficients of forces

and moments, they are primarily function of Mach number, Reynolds number, angle of attack

and side slip angle and are secondary functions of time rate of change of side slip angle and

angle of attack.

These coefficients are calculated using MISSILE DATCOM program which is necessary to

quickly and economically estimate the aerodynamics of a wide variety of missile

configuration designs [2, 8]. The fundamental purpose of MISSILE DATCOM is to provide

an aerodynamic design tool which has the accuracy suitable for preliminary design, and the

capability for the user to easily substitute methods to fit specific applications [9].

Inputs to the program are grouped by "case". A "case" consists of a set of input cards which

define the flight conditions and geometry to be run. Provisions are made to allow multiple

cases to be run. The output file has three main sections: First, an analysis by the input error

checking routine is provided. It lists all input cards provided by the user and identifies any

input errors detected. Second, a listing of all input cards, grouped by case, are provided;

included in this output is an error analysis from the major input error routine MAJERR.

Finally, the total configuration aerodynamics is provided in summary form; one page of

aerodynamic output is supplied for each Mach number specified. The MAJERR results and

the total configuration aerodynamics results are listed in succession for each case [9]. The

following figures (Fig.2.a-e) show the aerodynamic coefficient curves for the model bomb

under study.

Fig.2a: Lift Coefficient

Fig.2b: Drag coefficient

Fig.2c: Side Force coefficient

-4

-2

0

2

4

-40 -20 0 20 40

Cz

α

0

0.5

1

1.5

2

2.5

-40 -20 0 20 40

Cx

α

-1.5

-1

-0.5

0

0.5

1

1.5

-15 -10 -5 0 5 10 15

Cy

β


Fig.2d: Pitch moment coefficient

Fig.2e: Yaw moment coefficient

4. Wind disturbance model

Wind with its stochastic nature has an effect on the bomb flight parameters. This wind affects

the relative velocity of body with respect to surrounding air and hence affects the

aerodynamic forces and moments acting on bomb. In this paper we are not concerned with

studying the wind itself, but its influence on bomb trajectory. To generate a turbulence signal

with the correct characteristics, a unit variance, band-limited white noise signal is passed

through or used in the appropriate filters. These filters are ultimately derived from the

turbulence spectra.

Three forms of filters are covered in the military references MIL-HDBK-1797 and

MIL-F-8785C [4, 5 and 6]:

Continuous Von Kármán,

Continuous Dryden, and

Discrete Dryden.

Components of wind using Continuous Dryden Spectrum are shown in Fig.3.

Fig.3: Wind components

5. Simulation Results

Release of bomb is simulated using MATLAB and SIMULINK. First, simulation results were

compared against reference data, part of these data is in reference [11], to validate the

constructed model, and then we study the effect of disturbance on bomb trajectory.

-1

-0.5

0

0.5

1

-40 -20 0 20 40

Cm

α

-3

-2

-1

0

1

2

-15 -10 -5 0 5 10 15

Cn

β


Case I: Bomb flight evaluation

The bomb is released at different velocities (100[m/sec], 200[m/sec] and 300[m/sec] ) each at

different altitudes (300[m] to 3300[m]) and compared with reference data.

Fig.4: Release curves results vs. reference data

The percentage range error in simulation results does not exceed ±2% when bomb is released

from altitudes (300[m]to3300[m]) . Fig.4 shows the percentage error in range.

Fig.5: Percentage error in range

Case II: Bomb release simulation in windy environment

It was assumed that a bomb is released from altitude 1500[m], and the aircraft kept flying at

speed 250[m/sec]. Subsequent figures (Fig.6.a-g) present the flight trajectory and flight

parameters against time and windy environment effect on bomb flight.


Fig.6a: Effect of wind on bomb longitudinal and lateral path

Fig.6b: Effect of wind on bomb trajectory

Fig.6c: Effect of wind on bomb velocity


Fig.6d: Effect of wind on bomb pitch angle

Fig.6e: Effect of wind on bomb yaw angle

Fig.6f: Effect of wind on bomb angle of attack


Fig.6g: Effect of wind on bomb sideslip angle

From the previous figures, it is clear that wind affects bomb flight parameters. Figures

(Fig.6.a and Fig.6.b) show the bomb trajectory in air and the effect of wind on bomb

trajectory shape. Fig.6.c shows the effect of wind on velocity where its value in windy

environment vibrates around its value in no-turbulence. Also, the wind affects the value of

pitch angle as it swings about its value in no- turbulence curve (Fig.6.d). Figures (Fig.6.e-g)

show the wind effect on the behavior of yaw angle, angle of attack and sideslip angle that

posses oscillations due to wind and make bomb deviates from vertical plane of release, but the

bomb remains stable.

6. Conclusion

A 6DOF nonlinear dynamic model of bomb had built to simulate the bomb trajectory. The

MISSILE DATCOM program is used to get aerodynamic coefficients of bomb configuration.

In addition to MISSILE DATCOM, MATLAB is used to simplify, accelerate the modeling

process and create open loop model. This open loop model is required for analysis and in

future use in modeling flight bomb dynamics and control system design. The conducted

analysis has proved that the effect of wind on the accuracy of bomb release is essential and

should be taken into account when planning the bombing.

References

[1] Kowaleczko, G., Zyluk, A., “Influence of Atmospheric Turbulence on Bomb Release,” ”,

Journal of Theoretical and Applied Mechanics, JTAM-47,” Warsaw, 2009, pp. 69-90.

[2] Mansor, S., Ishak, I.S., Omar, W.Z., Rahman, A.B., Shamsudin, M.A., “Evaluation of

Aerodynamic Derivatives of MK82 Bomb from Wind Tunnel Testing and Empirical

Methods,” ”, International Conference on Mechanical, Automotive and Aerospace

Engineering, ICMAAE-2,” July 2013.

[3] Chand, K.K., Panda, H.S., “Mathematical Model to Simulate the Trajectory Elements of

an Artillery Projectile Proof Shot,” ”, Defense Science Journal,” Jan 2007, pp. 139-148.

[4] Gage, S., “Creating a Unified Graphical Wind Turbulence Model from Multiple

Specifications,” ”, AIAA Modeling and Simulation Technologies Conference and Exhibit,

AIAA 2003-5529”, August, 2003.

[5] U.S. Military Handbook MIL-HDBK-1797, 19December 1997.

[6] U.S. Military Specification MIL-F-8785C, 5 November 1980.

[7] Saad, M., “Flight Control System Design and Simulation,”,” Military Technical Collage,

M.Sc.” Cairo, 2013.


[8]Elharouny, A. S., Youssef, A.M., Zakaria, M.Y., Abdelhameed, M.M., “Procedures For

Building Aerodynamic Models for Small Unmanned Aerial Vehicle,” ”, Proceeding of the

International Conference on Applied Mechanics and Mechanical Engineering, AMME-15”

May, 2012.

[9] Blake, W.B.,”Missile Datcom, User’ Manual-1997 FORTRAN 90 Revision”,

AFRL-VA-WP-TR-1998-3009, Feb, 1998.

[10] Shilo, M.A. “Six Degree of Freedom Flight Dynamic Model of MK82 Store”, “Defense

Science and Technology Orgnisation, Aeronautical Research Laboratory, Victoria”, Jan,

1994.

[11] Marvin, k., Wrenn, A., “MK81 and Mk82 Bomb Release Curves”, “United States

Orgnisation Laboratory, NOLTR 65-230”, May, 1966.

[12] Gkritizapis, D.N., Panagiotopoulos, E.E., Margaris, D.P., Papanikas, D.G., “Modified

Linear Theory for Spinning or Non-spinning Projectile”, “The Open Mechanics Journal”, Jan,

2008, pp. 6-11.

[13] Arnold, R.J., Knight, J.B., “Weapon Delivery and Ballistic Flight Testing”, “Flight test

technique series, VOL-10”, July, 1992.

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